What causes this different bone influence?
Your first bone, called Bone, is the parent of all the bones, so, when you move it, it will move the part of the mesh it is supposed to influence, but it will also move all its children bones and therefore all the parts of the mesh that these other bones influence.
When you move the small bone, called Bone.001, it only moves itself + the part of the mesh it influences.
If you want each bone to influence its own part of the mesh and be independent you need to unparent with altP &gt; Unparent.
If you need a root bone, create a new bone wherever you want next to the others. Select this bone and go in the Properties panel &gt; Bone, deactivate the Deform option. Now, to parent all the other bones to this one: select them all, select the root at the end, press CtrlP &gt; Keep Offset.